Low noise amplifiers are frequently used in various electronic devices. A fundamental characteristic of such amplifiers is linearity.
A low noise amplifier can be considered as a non-linear system whose input-output characteristic can be modeled by a series of powers truncated at the third order. If the input signal Vi is constituted by two tones at respective frequencies ω1 and ω2, i.e., Vi=A1×cos(ω1×t)+A2×cos(ω2×t) with ω1 almost the same as ω2, with ω1=ω and ω2−ω1<<ω and A1=A2, we have linearity that can be characterised by a parameter of intermodulation of the third order IM3 in relation to a certain level of power of the two input tones or by the intercept of the third order IP3. In fact we have
  IM3  =      10    ⁢                  ⁢    log    ⁢          P3      P1      where with P1 the power of the tone at ω1 is indicated while with P3 the power of the spurious tones at 2ω2−ω1 or at 2ω1−ω2 is indicated. As in a real amplifier the two spurious tones do not necessarily have equal Amplitude. There are two different IM3, i.e., the IM3low referred to the spurious tone 2ω2−ω1 and the IM3high referred to the spurious tone 2ω1−ω2 with IM3 being the maximum between IM3high and IM3low. The intercept of the third order IP3 of a non-linear system is linked to the parameter IM3 by the relation:
      IIP3    ⁡          [      dBm      ]        =            Pi      ⁡              [        dBm        ]              -                  IM3        ⁡                  [          dB          ]                    2      where IIP3 is the intercept of the third order in input to the non-linear system and Pi is the power of the signal in input to said non-linear system; since in a real amplifier we have the parameters IM3high and IM3low, we also have the parameters IIP3high and IIP3low: In addition we have that the intercept of the third order OIP3 relative to the signal in output from the linear system is given by:OIP3[dBm]=IIP3[dBm]+G[dB]where G is the gain in decibels of said non-linear system. For OIP3 we have the parameters OIP3high and OIP3low.
A low noise amplifier that presents good performance in terms of linearity is shown in the article “Effect of out-of-band termination on intermodulation distortion in common-emitter circuits”, IEEE MTT-S Dig., vol. 3, pages 977-980, June 1999 by V. Aparin and C. Persico. The low noise amplifier described comprises a bipolar transistor in common-emitter configuration and particular circuits for the polarization of the transistor, for the input adaptation and for the output adaptation. The parameter IM3 calculated for a bipolar transistor Q1 in common-emitter configuration, shown in FIG. 1, depends on numerous factors amongst which the impedances of input Z1, of load Z3 and of degeneration of emitter Z2. If the signal in input to the transistor Q1 is constituted by two tones at frequencies ω1 and ω2, we have that the parameter IM3 depends on values Z1, Z2 and Z3 at the frequency Δω and at the frequency 2ω where the frequency ω is equal to the frequency ω1 and almost the same as the frequency ω2 and Δω=ω2−ω1<<ω. Therefore by suitable choosing the values Z1, Z2 and Z3 it is possible to minimize the parameter IM3 without influencing the performance of the circuit at the operative frequency ω.
FIG. 2 shows the implementation of a low noise amplifier described in the abovementioned article. In the circuit topology described it is possible to set independently one from the other the values of the input impedance Zs at different frequencies, that is at the operative frequency ω (Zs((ω)), at low frequency Δω (Zs(Δω)), and at double the operative frequency 2ω (Zs(2ω)). The amplifier of FIG. 2 comprises a bipolar transistor Q2 and inductances Lb, Lc and Le connected to the respective base terminals, collector and emitter. The inductance Le is connected to a terminal of a microstrip ML4 having the other terminal connected to ground while the inductance Lc is connected to the supply voltage Vcc by means of the parallel of a resistance R3 and of another microstrip ML5. The inductance Lc is connected to the output terminal OUT by means of the series of an inductance L1 and a capacitance C5 in which another capacitance C4 is connected between the terminal in common of the inductance L1 and of the capacitance C5 and ground. The inductance Lb is connected to the supply voltage Vcc by means of the series of another microstrip ML3, a resistance R1 and a resistance R3; between the terminals of the resistance R1 and ground two capacitances C3 and C2 are positioned. The inductance Lb is connected to the input terminal IN by means of the series of another microstrip ML2 and of a capacitance C1; another microstrip ML1 is positioned between the terminal IN and ground. The capacitance C3 has a much higher value than the capacitances C1 and C2.
At the frequency Δω, since the capacitance C3 is a short circuit, the capacitances C1 and C2 are open elements and the values of the impedance offered by the inductance Lb and by the microstrip ML2 are almost nil, we have the input impedance Zs(Δω) that is equal to the resistance R1.
At the frequencies ω and 2ω the capacitances C1 and C2 have negligible impedances while the microstrip ML1, having length l1=λ/4, behaves like an open circuit at the frequency ω and like a short circuit at the frequency 2ω. Therefore at the frequency ω the impedance Zs depends on the inductance Lb and on the length l3 of the microstrip ML3. At the frequency 2ω the impedance Zs depends on the inductance Lb, on the length l2 of the microstrip ML2 and on the length l3 of the microstrip ML3. Setting the length l3 and the inductance Lb at the operative frequency ω the resistance R1 and the length l2 of the microstrip ML2 can be chosen to vary the impedance Zs at the frequencies Δω and 2ω to obtain the maximum linearity. The microstrip ML5, having length λ/4, behaves like an open circuit at the frequency ω and like a short circuit at the frequencies Δω and 2ω. Such a low noise amplifier has the disadvantages of poor insulation between input and output, a low stability and the interdependence between the output adaptation and that in input.